Let R be a relation on the set N≥0 given byR = {(a, b) : (b − a) is divisible by 6}Show that this is an equivalence relation
Question
Solution 1
To show that a relation is an equivalence relation, we need to prove that it is reflexive, symmetric, and transitive.
- Reflexive: A relation R is reflexive if for every a in N≥0, (a, a) is in R. In this case, (b - a) would be (a - a) which equals 0. Since 0 is divisible by 6, the relation is refl Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
Similar Questions
Let R be a relation on the set N≥0 given byR = {(a, b) : (b − a) is divisible by 6}Show that this is an equivalence relation
f A={1,4,5} and the relation R defined on the set A as aRb if a+b < 6 checkwhether the relation R is an equivalence relation
Let R be a relation on the set N of natural numbers defined by nRm Û n is a factor of m (i.e., n|m). Then R is
Let R be the relation on the set Z defined by xRy iff x − y is an integer. Prove that R is anequivalence relation on Z.
Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.